maxpool

Pool data to maximum value

Syntax

Y = maxpool(X,poolsize)

[Y,indx,inputSize] = maxpool(X,poolsize)

Y = maxpool(X,'global')

___ = maxpool(___,'DataFormat',FMT)

___ = maxpool(___,Name,Value)

Description

The maximum pooling operation performs downsampling by dividing the input into pooling regions and computing the maximum value of each region.

The maxpool function applies the maximum pooling operation to dlarray data. Using dlarray objects makes working with high dimensional data easier by allowing you to label the dimensions. For example, you can label which dimensions correspond to spatial, time, channel, and batch dimensions using the "S", "T", "C", and "B" labels, respectively. For unspecified and other dimensions, use the "U" label. For dlarray object functions that operate over particular dimensions, you can specify the dimension labels by formatting the dlarray object directly, or by using the DataFormat option.

Note

To apply maximum pooling within a dlnetwork object, use one of these layers:

• maxPooling2dLayer

• maxPooling3dLayer

Y = maxpool(X,poolsize) applies the maximum pooling operation to the formatted dlarray object X. The function downsamples the input by dividing it into regions defined by poolsize and calculating the maximum value of the data in each region. The output Y is a formatted dlarray with the same dimension format as X.

The function, by default, pools over up to three dimensions of X labeled "S" (spatial). To pool over dimensions labeled "T" (time), specify a pooling region with a "T" dimension using the PoolFormat option.

For unformatted input data, use the 'DataFormat' option.

[Y,indx,inputSize] = maxpool(X,poolsize) also returns the linear indices of the maximum value within each pooled region and the size of the input feature map X for use with the maxunpool function.

Y = maxpool(X,'global') computes the global maximum over the spatial dimensions of the input X. This syntax is equivalent to setting poolsize in the previous syntaxes to the size of the 'S' dimensions of X.

___ = maxpool(___,'DataFormat',FMT) applies the maximum pooling operation to the unformatted dlarray object X with format specified by FMT using any of the previous syntaxes. The output Y is an unformatted dlarray object with dimensions in the same order as X. For example, 'DataFormat','SSCB' specifies data for 2-D maximum pooling with format 'SSCB' (spatial, spatial, channel, batch).

___ = maxpool(___,Name,Value) specifies options using one or more name-value pair arguments. For example, 'PoolFormat','T' specifies a pooling region for 1-D pooling with format 'T' (time).

Examples

Perform 2-D Maximum Pooling

Create a formatted dlarray object containing a batch of 128 28-by-28 images with 3 channels. Specify the format 'SSCB' (spatial, spatial, channel, batch).

miniBatchSize = 128;
inputSize = [28 28];
numChannels = 3;
X = rand(inputSize(1),inputSize(2),numChannels,miniBatchSize);
dlX = dlarray(X,'SSCB');

View the size and format of the input data.

size(dlX)

ans = 1×4

    28    28     3   128

dims(dlX)

ans = 
'SSCB'

Apply 2-D maximum pooling with 2-by-2 pooling windows using the maxpool function.

poolSize = [2 2];
dlY = maxpool(dlX,poolSize);

View the size and format of the output.

size(dlY)

ans = 1×4

    27    27     3   128

dims(dlY)

ans = 
'SSCB'

Perform 2-D Global Maximum Pooling

Create a formatted dlarray object containing a batch of 128 28-by-28 images with 3 channels. Specify the format 'SSCB' (spatial, spatial, channel, batch).

miniBatchSize = 128;
inputSize = [28 28];
numChannels = 3;
X = rand(inputSize(1),inputSize(2),numChannels,miniBatchSize);
dlX = dlarray(X,'SSCB');

View the size and format of the input data.

size(dlX)

ans = 1×4

    28    28     3   128

dims(dlX)

ans = 
'SSCB'

Apply 2-D global maximum pooling using the maxpool function by specifying the 'global' option.

dlY = maxpool(dlX,'global');

View the size and format of the output.

size(dlY)

ans = 1×4

     1     1     3   128

dims(dlY)

ans = 
'SSCB'

Perform 1-D Maximum Pooling

Create a formatted dlarray object containing a batch of 128 sequences of length 100 with 12 channels. Specify the format 'CBT' (channel, batch, time).

miniBatchSize = 128;
sequenceLength = 100;
numChannels = 12;
X = rand(numChannels,miniBatchSize,sequenceLength);
dlX = dlarray(X,'CBT');

View the size and format of the input data.

size(dlX)

ans = 1×3

    12   128   100

dims(dlX)

ans = 
'CBT'

Apply 1-D maximum pooling with pooling regions of size 2 with a stride of 2 using the maxpool function by specifying the 'PoolFormat' and 'Stride' options.

poolSize = 2;
dlY = maxpool(dlX,poolSize,'PoolFormat','T','Stride',2);

View the size and format of the output.

size(dlY)

ans = 1×3

    12   128    50

dims(dlY)

ans = 
'CBT'

Unpool 2-D Maximum Pooled Data

Create a formatted dlarray object containing a batch of 128 28-by-28 images with 3 channels. Specify the format 'SSCB' (spatial, spatial, channel, batch).

miniBatchSize = 128;
inputSize = [28 28];
numChannels = 3;
X = rand(inputSize(1),inputSize(2),numChannels,miniBatchSize);
dlX = dlarray(X,'SSCB');

View the size and format of the input data.

size(dlX)

ans = 1×4

    28    28     3   128

dims(dlX)

ans = 
'SSCB'

Pool the data to maximum values over pooling regions of size 2 using a stride of 2.

[dlY,indx,dataSize] = maxpool(dlX,2,'Stride',2);

View the size and format of the pooled data.

size(dlY)

ans = 1×4

    14    14     3   128

dims(dlY)

ans = 
'SSCB'

View the data size.

dataSize

dataSize = 1×4

    28    28     3   128

Unpool the data using the indices and data size from the maxpool operation.

dlY = maxunpool(dlY,indx,dataSize);

View the size and format of the unpooled data.

size(dlY)

ans = 1×4

    28    28     3   128

dims(dlY)

ans = 
'SSCB'

Unpool 1-D Maximum Pooled Data

Create a formatted dlarray object containing a batch of 128 sequences of length 100 with 12 channels. Specify the format 'CBT' (channel, batch, time).

miniBatchSize = 128;
sequenceLength = 100;
numChannels = 12;
X = rand(numChannels,miniBatchSize,sequenceLength);
dlX = dlarray(X,'CBT');

View the size and format of the input data.

size(dlX)

ans = 1×3

    12   128   100

dims(dlX)

ans = 
'CBT'

Apply 1-D maximum pooling with pooling regions of size 2 with a stride of 2 using the maxpool function by specifying the 'PoolFormat' and 'Stride' options.

poolSize = 2;
[dlY,indx,dataSize] = maxpool(dlX,poolSize,'PoolFormat','T','Stride',2);

View the size and format of the output.

size(dlY)

ans = 1×3

    12   128    50

dims(dlY)

ans = 
'CBT'

Unpool the data using the indices and data size from the maxpool operation.

dlY = maxunpool(dlY,indx,dataSize);

View the size and format of the unpooled data.

size(dlY)

ans = 1×3

    12   128   100

dims(dlY)

ans = 
'CBT'

Input Arguments

X — Input data

dlarray

Input data, specified as a formatted or unformatted dlarray object.

If X is an unformatted dlarray, then you must specify the format using the DataFormat option.

The function, by default, pools over up to three dimensions of X labeled "S" (spatial). To pool over dimensions labeled "T" (time), specify a pooling region with a "T" dimension using the PoolFormat option.

poolsize — Size of pooling regions

positive integer | vector of positive integers

Size of the pooling regions, specified as a numeric scalar or numeric vector.

To pool using a pooling region with edges of the same size, specify poolsize as a scalar. The pooling regions have the same size along all dimensions specified by 'PoolFormat'.

To pool using a pooling region with edges of different sizes, specify poolsize as a vector, where poolsize(i) is the size of corresponding dimension in 'PoolFormat'.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'Stride',2 specifies the stride of the pooling regions as 2.

DataFormat — Description of data dimensions

character vector | string scalar

Description of the data dimensions, specified as a character vector or string scalar.

A data format is a string of characters, where each character describes the type of the corresponding data dimension.

The characters are:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, consider an array containing a batch of sequences where the first, second, and third dimensions correspond to channels, observations, and time steps, respectively. You can specify that this array has the format "CBT" (channel, batch, time).

You can specify multiple dimensions labeled "S" or "U". You can use the labels "C", "B", and "T" once each, at most. The software ignores singleton trailing "U" dimensions after the second dimension.

If the input data is not a formatted dlarray object, then you must specify the DataFormat option.

For more information, see Deep Learning Data Formats.

Data Types: char | string

PoolFormat — Description of pooling dimensions

character vector | string scalar

Description of pooling dimensions, specified as a character vector or string scalar that provides a label for each dimension of the pooling region.

The default value of PoolFormat depends on the task:

Task	Default
1-D pooling	"S" (spatial)
2-D pooling	"SS" (spatial, spatial)
3-D pooling	"SSS" (spatial, spatial, spatial)

The format must have either no "S" (spatial) dimensions, or as many "S" (spatial) dimensions as the input data.

The function, by default, pools over up to three dimensions of X labeled "S" (spatial). To pool over dimensions labeled "T" (time), specify a pooling region with a "T" dimension using the PoolFormat option.

For more information, see Deep Learning Data Formats.

Stride — Step size for traversing input data

1 (default) | numeric scalar | numeric vector

Step size for traversing the input data, specified as the comma-separated pair consisting of 'Stride' and a numeric scalar or numeric vector. If you specify 'Stride' as a scalar, the same value is used for all spatial dimensions. If you specify 'Stride' as a vector of the same size as the number of spatial dimensions of the input data, the vector values are used for the corresponding spatial dimensions.

The default value of 'Stride' is 1. If 'Stride' is less than poolsize in any dimension, then the pooling regions overlap.

The Stride parameter is not supported for global pooling using the 'global' option.

Example: 'Stride',3

Data Types: single | double

Padding — Size of padding applied to edges of data

0 (default) | 'same' | numeric scalar | numeric vector | numeric matrix

Size of padding applied to edges of data, specified as the comma-separated pair consisting of 'Padding' and one of the following:

• 'same' — Padding size is set so that the output size is the same as the input size when the stride is 1. More generally, the output size of each spatial dimension is ceil(inputSize/stride), where inputSize is the size of the input along a spatial dimension.

• Numeric scalar — The same amount of padding is applied to both ends of all spatial dimensions.

• Numeric vector — A different amount of padding is applied along each spatial dimension. Use a vector of size d, where d is the number of spatial dimensions of the input data. The ith element of the vector specifies the size of padding applied to the start and the end along the ith spatial dimension.

• Numeric matrix — A different amount of padding is applied to the start and end of each spatial dimension. Use a matrix of size 2-by-d, where d is the number of spatial dimensions of the input data. The element (1,d) specifies the size of padding applied to the start of spatial dimension d. The element (2,d) specifies the size of padding applied to the end of spatial dimension d. For example, in 2-D, the format is [top, left; bottom, right].

The 'Padding' parameter is not supported for global pooling using the 'global' option.

Example: 'Padding','same'

Data Types: single | double

Output Arguments

Y — Pooled data

dlarray

Pooled data, returned as a dlarray with the same underlying data type as X.

If the input data X is a formatted dlarray, then Y has the same format as X. If the input data is not a formatted dlarray, then Y is an unformatted dlarray with the same dimension order as the input data.

indx — Indices of maximum values

dlarray

Indices of maximum values in each pooled region, returned as a dlarray. Each value in indx represents the location of the corresponding maximum value in Y, given as a linear index of the values in X.

If X is a formatted dlarray, indx has the same size and format as the output Y.

If X is not a formatted dlarray, indx is an unformatted dlarray. In that case, indx is returned with the following dimension order: all 'S' dimensions, followed by 'C', 'B', and 'T' dimensions, then all 'U' dimensions. The size of indx matches the size of Y when Y is permuted to match the previously stated dimension order.

Use the indx output with the maxunpool function to unpool the output of maxpool.

indx output is not supported when using the 'global' option.

inputSize — Size of input feature map

numeric vector

Size of the input feature map, returned as a numeric vector.

Use the inputSize output with the maxunpool function to unpool the output of maxpool.

inputSize output is not supported when using the 'global' option.

Algorithms

Maximum Pooling

The maxpool function pools the input data to maximum values. For more information, see the 2-D Max Pooling Layer section of the maxPooling2dLayer reference page.

Deep Learning Array Formats

Most deep learning networks and functions operate on different dimensions of the input data in different ways.

For example, an LSTM operation iterates over the time dimension of the input data, and a batch normalization operation normalizes over the batch dimension of the input data.

To provide input data with labeled dimensions or input data with additional layout information, you can use data formats.

A data format is a string of characters, where each character describes the type of the corresponding data dimension.

The characters are:

• "S" — Spatial

• "C" — Channel

• "B" — Batch

• "T" — Time

• "U" — Unspecified

For example, consider an array containing a batch of sequences where the first, second, and third dimensions correspond to channels, observations, and time steps, respectively. You can specify that this array has the format "CBT" (channel, batch, time).

To create formatted input data, create a dlarray object and specify the format using the second argument.

To provide additional layout information with unformatted data, specify the formats using the DataFormat and PoolFormat arguments.

For more information, see Deep Learning Data Formats.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Code generation supports only 1-D and 2-D spatial and spatio-temporal data. Convolving over 3-D spatial and spatio-temporal data format such as "SSS" or "SST" is not supported.

• Code generation supports only channel-wise (depth-wise) separable convolution and regular convolution. Both NumChannelsPerGroup and NumFiltersPerGroup must be equal to 1.

• The input must be single underlying data type.

• The convolution dimensions must be fixed size.

• The dimension that corresponds to the channel in the input must be fixed size.

• The Stride, DilationFactor, Padding and PaddingValue name-value pairs must be compile-time constants.

• PaddingValue must be 0.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• Code generation supports only 1-D and 2-D spatial and spatio-temporal data. Convolving over 3-D spatial and spatio-temporal data format such as "SSS" or "SST" is not supported.

• Code generation supports only channel-wise (depth-wise) separable convolution and regular convolution. Both NumChannelsPerGroup and NumFiltersPerGroup must be equal to 1.

• The input must be single underlying data type.

• The convolution dimensions must be fixed size.

• The dimension that corresponds to the channel in the input must be fixed size.

• The Stride, DilationFactor, Padding and PaddingValue name-value pairs must be compile-time constants.

• PaddingValue must be 0.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

The maxpool function supports GPU array input with these usage notes and limitations:

• When the input argument X is a dlarray with underlying data of type gpuArray, this function runs on the GPU.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2019b

R2020a: maxpool indices output argument changes shape and data type

Starting in R2020a, the data type and shape of the indices output argument of the maxpool function are changed. The maxpool function outputs the indices of the maximum values as a dlarray with the same shape and format as the pooled data, instead of a numeric vector.

The indices output of maxpool remains compatible with the indices input of maxunpool. The maxunpool function accepts the indices of the maximum values as a dlarray with the same shape and format as the input data. To prevent errors, use only the indices output of the maxpool function as the indices input to the maxunpool function.

To reproduce the previous behavior and obtain the indices output as a numeric vector, use the following code:

[Y,indx,inputSize] = maxpool(Y,poolsize);
indx = extractdata(indx);
indx = reshape(indx,[],1);